The picture looks to me like the type of thing you would get if you crossed a lime with a citron (I mean a lemon with more C. medica ancestry than the usual lemon).
These were to comments made to the video-
"You are probably right about the 1st one, It's just a lemon but a 'desi' lemon and desi fruits are considered the one's grown in villages as apposed to the commercially grown ones. 2nd one is, as the other people pointed out is gondhoraj (gondho means smell/fragrance and raj mean king/royalty so basically king of fragrance), and the third one is kagzi lebu"
"Bangladeshi here, these are all recognized as different varieties of lime. B is called elachi lebu and C is called kagoji lebu in our regional dialect. these are used as you'd normally use lime, for enhancing the taste of curries and daals, for teas etc. My mom loves to use C for lemonade because it's very fragrant. also, we only eat the rind of B as it is very thick and less bitter, goes great with rice and curry."
